We calculate the fluctuations in the current and energy densities for the case of a quantized, minimally coupled, massless, complex scalar field around a straight and infinitesimally thin cosmic string carrying magnetic flux. At zero temperature, we evaluate the fluctuations in the current and energy densities for arbitrary flux and deficit angle. At a finite temperature, we evaluate the fluctuations in the energy density for the special case wherein the flux is absent and the deficit angle equals π. We find that, quite generically, the dimensionless ratio of the variance to the mean-squared values of the current and energy densities are of the order of unity, which suggests that the fluctuations around cosmic strings can be considered to be large.